Answer:
$595
Step-by-step explanation:
Local extreme Value for each of the Following A) F(x)=x^² - 4x² +5
Answer:
max{x²-4x²+5} = 5 at x = 0
Step-by-step explanation:
1. Find the critical numbers by finding the first derivative of f(x), set it to 0 and solve for x.
[tex]f'(x)=0[/tex]
We get:
[tex]f(x) = -3x^2+5\\f'(x) = -6x\\-6x = 0\\x = 0[/tex]
So the critical number is x = 0.
2. Evaluate the first derivative by plugging in the critical number and see if the derivative is positive or negative on both sides:
[tex]f'(x)[/tex] is positive when the x < 0 (for example: -6*(-1)=+)
[tex]f'(x)[/tex] is negative when the x > 0 (for example: -6*(1)=-)
Therefore, you have a local maximum.
Now just get the Y value by plugging in the critical number in the original function. [tex]f(0)=5[/tex]
local maximum is (0,5)
The graph below represents which of the following functions?
-12
-10
OA.
OB.
O C.
D.
4
F(x) =
[[|-*|× <1}
(x+4×21}
F(x) =
F(x) =
F(x) =
{/4-x²|x<2}
x2 2f
X
14-x²|x> 21
x x≤ 2}
2}
XS
{|-*² |× > 3)
(x+4× ≤3)
10
12
C
Answer: B
Step-by-step explanation:
The parabola has an open hole at x=2, and the line has a closed hole at x=2.
This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].
This eliminates everything except for B.
Which transformations must be applied to object A to place it in the position of object B?
rotation and reflection
rotation and translation
reflection and translation
rotation, reflection, and translation
In order for object A to be placed in the position of object B, there needs to be a rotation and translation.
How would object A get to object B?The first step would be to rotate object A to the left to give it the same orientation as object B.
Then, translate object A to the coordinates of object B. This would lead to object A fitting into object B.
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Harry is building a decking area in his garden.
250 cm
150 cm
4 m
7m
150 cm
He needs to build a wooden frame in the shape of the decking.
Calculate the perimeter of the decking area.
The perimeter of the decking area is 800cm.
How to determine the perimeterIt is important to note that the decking area takes the shape of a rectangle
The formula for determining the perimeter of the decking area is given as;
Perimeter = 2 multiplied by the sum of the length and width of the rectangle
It is mathematically written as;
Perimeter = 2 ( length + width)
Where;
length = 250cmwidth = 150 cmNow, let's substitute the values into the formula
Perimeter = 2 ( 150 + 250)
Sum the bracket
Perimeter = 2 ( 400 )
Perimeter = 2 × 400
Perimeter = 800 cm
Thus, the perimeter of the decking area is 800cm
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4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the diameter of the circle x² + y² - 4x - 4y +4= 0
The standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .
How to find the standard equation of a hyperbolaIn this problem we must determine the equation of the hyperbola in its standard form from the coordinates of the foci and a general equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:
(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)
(h, k) = (2, 2)
To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the general equation of the circle into its standard form.
If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:
x² + y² - 4 · x - 4 · y + 4= 0
(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4
(x - 2)² + (y - 2)² = 2²
The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:
V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)
And the distance from the center to any of the vertices is 2 (semi-major distance, a) and the semi-minor distance is:
b = √(c² - a²)
b = √(3² - 2²)
b = √5
Therefore, the standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .
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Solve the following system of equations
y= -½/x-2
Answer:
Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints.
Step-by-step explanation:
Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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the graph shown below expresses a redical function that can be written in the form f(x)= a(x+k)^1/n + c. what does the graph tell the value of a in this function?
The value of n given the form of the function is (b) positive odd number
How to interpret the graph?The form of the graph is given as:
f(x) = a(x + k)^1/n + c
For the given graph, we have the following features:
a > 0 --- a is positive
k > 0 --- k is positive
c < 0 --- c is negative
If n is an even number, the function would be undefined because the even root of a number is undefined
However, the function is defined if n is an odd number,
Hence, the value of n given the form of the function is a positive odd number
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In exercises 21 and 22, point B is between A and C on Line AC. Use the information to write an equation in terms of x. Then solve the equation and find AB, BC, and AC. AB= 13+ 2x BC= 12 AC= x+2
The value of x is -23 and the values of AB, BC, and AC are -33, 12 and -21
How to solve the equation and find AB, BC, and AC?The equations are given as
AB = 13 + 2x
BC = 12
AC = x + 2
Point B is between A and C on Line AC.
So, we have
AC = AB + BC
This gives
x + 2 = 13 + 2x + 12
Evaluate the like terms
x - 2x = 13 + 12 - 2
This gives
-x = 23
Divide by -1
x =-23
Substitute x =-23 in AB = 13 + 2x and AC = x + 2
AB = 13 - 2 * 23 = -33
AC = -23 + 2 = -21
Hence, the value of x is -23 and the values of AB, BC, and AC are -33, 12 and -21
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You are loading a rental truck with 78-pound boxes and have
60 boxes to load. If the empty truck weighs 8840 pounds,
then the equation W=78b+8840 gives the total weight of
the truck if it is carrying b boxes.
Suppose the truck is not legally allowed to weigh more than
13,200 pounds.
Will your rental truck be able to legally carry the load of 60
boxes?
Explain why you answered yes or no and show all work.
Answer:
13200 needs to be less than 78*60+8840,
which is false because 13200 < 13520
Step-by-step explanation:
The truck cannot load 60 boxes as it exceeds the weight limit.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
W=78b+8840
So, b= 60
W= 78 x 66 + 8840
W = 5148 +8840
W = 13988 > 13200 ( limit for the weight)
Hence, the truck cannot load 60 boxes as it exceeds the weight limit.
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Which represents an exterior angle of triangle ABF?
∠BAD
∠AFE
∠CAD
∠CAB
The angle that represents an exterior angle of the given triangle is: D. ∠CAB.
What is an Exterior Angle of a Triangle?An exterior angle of a triangle is the angle that is located outside a triangle on an extended adjacent side of the triangle.
In the image given, and considering the options we have, ∠CAB is located outside a triangle ABF on an extended adjacent side CF of the triangle.
Therefore, the answer is: D. ∠CAB.
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Need help with this math question
The correlation coefficient is -0.87; strong correlation
How to determine the correlation coefficient?The given parameters are:
x = Time spent working out
y = lbs Overweight
Next, we enter the table of values in a graphing tool.
From the graphing tool, we have the following summary:
X Values
∑ = 27.1Mean = 2.71∑(X - Mx)2 = SSx = 22.569Y Values
∑ = 89Mean = 8.9∑(Y - My)2 = SSy = 778.9X and Y Combined
N = 10∑(X - Mx)(Y - My) = -114.19R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -114.19 / √((22.569)(778.9))
r = -0.8613
Approximate
r = -0.87
This means that the correlation coefficient is -0.87
Also, the correlation coefficient is a strong correlation, because it is closer to -1 than it is to 0
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Grocer Edwards graphs the relationship between the
diameter and heights of different cans in his store. The
graph is below.
Height (cm)
18-
D
16+
14+
12+
10+
8+
6+
4+
2+
2
Choose 1 answer:
4
●
6
8
A
●
10 12
What is the meaning of point A?
●
Diameter (cm)
●
14 16 18
A can with an 10 cm diameter has an 18 cm height.
A can with an 18 cm diameter has an 11 cm height.
A can with an 11 cm diameter has an 18 cm height.
A can with an 18 cm diameter has an 10 cm height.
Considering the given graph, the meaning of point A is given by:
A can with an 11 cm diameter has an 18 cm height.
What does the graph gives?The graph gives the height of the can as a function of the diameter. Both measures are in cm. Then, the axis are given as follows:
The x-axis is the diameter.The y-axis is the height.Point A has coordinates (11,18), that is, x = 11, y = 18, hence the interpretation is:
A can with an 11 cm diameter has an 18 cm height.
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Answer:
A
Step-by-step explanation:
just took the quiz and can confirm the other guy is valid :D
the sum of two numbers is 55 and the difference is 15 what are the numbers
[tex]x + y = 55 \\ x - y = 15 \\ \\ 2x = 70 \: \: \: \: \: \: x = 35 \\ y = 55 - x = 55 - 35 = 20[/tex]
Find the measure of a
Answer:
112°
Step-by-step explanation:
Angles on a line add to 180°.
Solve the following problems using Pythagoras. Include a diagram . a. How long must a ladder be to reach 12 ft up the wall, if thefoot of the ladder is placed 2.5 ft away from the wall
Answer:
sqrt(601)/2 ft
Step-by-step explanation:
The legs of the right triangle are 12 and 2.5. by the Pythagorean Theorem, the length of the ladder is sqrt(12^2 + 2.5^2) = sqrt(150.25). Simplified is sqrt(601)/2 ft.
The length of ladder used is 12.25 ft.
What is Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .
The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
example:
The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.
Solution:
Given : Hypotenuse = 16 units
Let us consider the given side of a triangle as the perpendicular height = 8 units
On substituting the given dimensions to the Pythagoras theorem formula
Hypotenuse^2 = Base^2 + Height^2
16^2 = B^2 + 8^2
B^2 = 256 - 64
B = √192 = 13.856 units
Therefore, the measure of the third side of a triangle is 13.856 units.
given:
base= 2.5 ft,
perpendicular= 12 ft
Using Pythagoras theorem,
H² = B² + P²
H² = 2.5² + 12²
H² = 6.25+ 144
H= 12.25 ft
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True or False - All whole numbers are integers but not all integers are whole numbers
Answer:
false
correct me if i'm wrong :]
Answer:
True
Step-by-step explanation:
the picture is the explanation and pretty much sus everything up about integers
please help me on this question!!
Answer:
B
Step-by-step explanation:
The domain is the set of input values, which is typically shown on the horizontal axis.
The answer is B.
The domain of the function refers to the possible values of the horizontal axis of the graph.
Hence, the domain is : 6 ≤ g ≤ 12
Select the story problem that this division problem represent 1/2 2/5
The story that the fraction given represents is that A. A whiteboard is 2/5 Meyer long and has na area of 1/3 square meter. How wide is the whiteboard?
How to illustrate the fraction?From the information given, it should be noted that the fraction given is 1/2 ÷ 2/5.
Therefore, this is represented by the story that a whiteboard is 2/5 Meyer long and has na area of 1/3 square meter. How wide is the whiteboard?
In conclusion, the correct option is A.
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The story problem that this division problem represent 1/2 ÷ 2/5 is a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the white board and is denoted as option A.
What is a Fraction?This is a description which represents a part of a whole.
The area of a rectangular shape of length L and width W is:
A = L×W
W=A/L
Only option A uses 1/2 as the area of the whiteboard and 2/5 is the other side of the board.
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Saca la medida de la pala superior e inferior con respecto a las siguientes medidas
*No son de la misma medida*
La pala inferior y la pala superior tienen longitudes verticales de 55 y 65 centímetros, respectivamente. No es posible encontrar las longitudes horizontales.
¿Cuáles son las medidas de la pala superior y la pala inferior de un arco compuesto?
En esta pregunta debemos saber interpretar las dimensiones geométricas de un arco compuesto y determinar las longitudes de cada pala. Primero, determinamos las longitudes verticales de cada una:
Pala inferior
i = 65 cm - 10 cm
i = 55 cm
Pala superior
s = 65 cm
La insuficiencia de datos sobre longitudes horizontales no permite obtener las longitudes horizontales de cada pala.
La pala inferior y la pala superior tienen longitudes verticales de 55 y 65 centímetros, respectivamente. No es posible encontrar las longitudes horizontales.
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helpppp meeeeee
Which expression represents the following statement? Add 8 to 6 times the quotient of 21 and 3.
6 x (21 ÷ 3) + 8
6 + 8 − (21 ÷ 3)
21 ÷ 3 − (8 + 6)
6 x (21 + 3) + 8
Answer:
(a) 6 x (21 ÷ 3) + 8
Step-by-step explanation:
The first step in translating English to math is to understand the English.
Parsing itThe quotient of 21 and 3 is written (21 ÷ 3). Six times that quotient is ...
6×(21÷3)
When 8 is added to this, it becomes ...
6 × (21 ÷ 3) + 8
1) A random sample of n = 12 individuals is selected from a population with
µ = 70 and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be M = 74.5 with S = 5.20
Based on the sample data, does the treatment have a significant effect.?
Use a two tailed test with α = 0.05
steps
a) State the Null and the Alternate Hypotheses
A random sample of n = 12 individuals is selected from a population with
µ = 70 and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be M = 74.5 with S = 5.20. Based on the sample data, the treatment has a significant effect as per the deduced test statistic. Following are the statements for Null and the Alternate Hypotheses,
H₀: The treatment does not have a significant effect
Hₐ: The treatment has a significant effect
According to the given information,
Size of the sample, n = 12
Population Mean, μ = 70
Sample Mean, M = 74.5
Standard Deviation, S = 5.20
The Null hypothesis is given by,
H₀: The treatment does not have a significant effect (μ = 70)
The Alternate hypothesis is given by,
Hₐ: The treatment has a significant effect (μ ≠ 70)
Since the population standard deviation is unknown, we will use one-sample t-test here.
Test statistic, TS = (M-μ) / (s/√n)
Substituting the given values of M, μ, S, and n, we get,
TS = (74.5-70) / (5.20/√12)
TS = 4.5 / 1.5
TS ≈ 3
The t table now provides critical values of -2.131 and 2.131 at 15 degrees of freedom for a two-tailed test using α = 0.05 (significance level).
Since our test statistic, TS does not fall in the range of the critical values, it falls in the rejection region. Thus, we can reject the null hypothesis and say that the treatment has a significant effect.
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you deposit 2000 in an account earning 3% interest compounded monthly.
a. how much will you have in the account in 20 years
b. how much interest will you earn
Answer:
a. 3641.51
b. 1641.51
Step-by-step explanation:
The future value formula will tell you the amount in the account in 20 years.
FormulaFV = P(1 +r/n)^(nt)
Principal P is compounded n times per year at annual rate r for t years.
ApplicationThe future value of the account with P=2000, r=0.03, n=12, and t=20 will be ...
FV = 2000(1 +0.03/12)^(12·20) = 2000(1.0025^240) ≈ 3641.50999
a.The account value in 20 years will be 3641.51.
b.The first 2000 of account value is the principal, so the interest is ...
interest = 3641.51 -2000
interest = 1641.51
__
Additional comment
Many calculators and all spreadsheets have built-in capability for making this calculation.
− 2 x − 2 > 4 OR − 8 x − 7 ≤ − 23
interval notaton and plot on line graph
The interval notation of the possible values of x according to.the given inequalities is; -3 > x and x>= 2.
What is the interval notation of the inequalities given in the task content?The interval notation of the given inequalities which describes the possible value of x according to the task content are as follows;
For − 2 x − 2 > 4; we have;
− 2 x > 4 +2
-2x > 6
x < -3.
For − 8 x − 7 ≤ − 23; we have;
− 8 x ≤ − 23 +7
-8x ≤ -16
x >= 2.
Consequently, the interval notation of the given inequalities is; -3 > x and x >= 2.
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A Food Marketing Institute found that 29% of households spend more than $125 a week on groceries. Assume the population proportion is 0.29 and a simple random sample of 207 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?
There is a ___ probability that the sample proportion of households spending more than $125 a week is less than 0.31. Round the answer to 4 decimal places.
Using the normal distribution, there is a 0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The estimate and the sample size are:
p = 0.29, n = 207.
Hence the mean and the standard error are given as follows:
[tex]\mu = p = 0.29[/tex].[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.29(0.71)}{207}} = 0.0315[/tex].The probability that the sample proportion of households spending more than $125 a week is less than 0.31 is the p-value of Z when X = 0.31, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.31 - 0.29}{0.0315}[/tex]
Z = 0.63
Z = 0.63 has a p-value of 0.7357.
0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
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Find the indicated side of the
right triangle.
60°
30°
X
x = 3√√√/[?]
3
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
The given is a special right triangle with angle measures 30-60-90
The measure of side lengths for this special right triangle are represented with
a-a[tex]\sqrt{3}[/tex]-2a respectively
Now, since the side length that sees angle measure 30 is given as 3 (represented with a) then the measure of the side length that sees angle measure 60 would be [tex]3\sqrt{3}[/tex]
In June 2020, Parks Canada closed the Bow Valley Parkway (Highway 1A) to vehicle traffic
between Banff and Castle Junction near Johnston Canyon. This made for a bike ride that cut
through a small piece of Canada’s beautiful Rocky Mountains. A group of friends decide to cycle
the trip, 25 km each way, from Banff to Johnston Canyon and back. They ride towards Johnston
Canyon straight into the wind, and then have the wind at their backs on the return trip. The wind
adds or subtracts 5 km/h from their speed. If the group of friends wants to complete the round trip
in 3 hours, algebraically find the average speed with no wind the group needs to cycle. Complete
the distance speed time chart to help solve the question. Round your answer to the nearest
hundredth of a km/h.
The average speed with no wind that the group needs to cycle between Banff and Castle Junction is 16.67 km/h.
What is the average speed of travel?The average speed (S) of travel is the distance (D) traveled divided by the time taken(T).
What is an algebraic equation?An algebraic equation is a statement of the equality of two expressions that have variables, using algebraic operations, known as addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
Data and Calculations:Distance to Castle Junction and from Banff = 50 km (25 x 2)
Time required to cycle = 3 hours
Effect of wind on cyclists = -+5 km/h
The algebraic equation for speed, S, is D/T
Where:
D = Total distance
T = Total time
Therefore, S = D/T = 50/3
S = 16.6667 km/h
Thus, the average speed with no wind that the group needs to cycle between Banff and Castle Junction is 16.67 km/h.
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Sequence: 15, 19, 23, 27,...
an an-1 +4
C
a1
=
The recursive function o f the given sequence will be an = an-1 + 4
Recursive functionThe formula for calculating the recursive function of n arithmetic sequence is expressed as
an = an-1 + d
Determine the common difference
d = 19 - 15 = 23 -19
d = 4
The recursive function o f the given sequence will be an = an-1 + 4
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12. The brakes on a vehicle can slow it down at a rate of 15m/s 2. Remember that slowing down is also a rate of change of speed. If this vehicle is travelling at 40 m/s how long would it take the brakes to bring the vehicle to a standstill? Show all steps and formulae used
Step-by-step explanation:
there are several formulas that could play a role.
but in our case, where we have velocities and the deceleration, we are going to use
fV = iV + at
fV = final velocity (0 on our case)
iV = initial velocity (40 m/s in our case)
a = acceleration (-15 m/s² in our case)
t is the time it takes to reach fV.
0 = 40 + (-15)t = 40 - 15t
15t = 40
3t = 8
t = 8/3 = 2.666666666... seconds
so, it takes 2.6666666... or 2 2/3 seconds to bring the vehicle to a standstill.
Which graph is the result of reflecting f(x) = (8)* across the y-axis and then across the x-axis? O 8- 6- 8 7
I assume you meant [tex]f(x)=8^x[/tex].
Reflecting across the x-axis would give [tex]y=-8^x[/tex].
Reflecting across the y-axis would give [tex]y=8^{-x}[/tex].